Rawls claimed that public reason is complete; that is, it allows citizens to formulate a reasonable answer to controversial institutions and laws through judgments that appeal to shared political values and reasoning methods. The aim of this paper is to examine the meaning of the completeness of public reason by discussing the dispute over the legalization of same-sex marriage. I will point out that various political conceptions of justice may lead to different, reasonable, orderings of political values. Moreover, the conception of public reason cannot resolve the background question, "What is marriage?" Therefore, the meaning of the completeness of public reason cannot be understood as "achieving consensus" on controversial issues. Public reason is complete in the sense of "achieving an institutional solution that can be reasonably accepted." To this end, it is necessary to supplement the democratic majority and legislative moral compromise based on ideals of public reason.